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Definition of carrot noun from the Oxford Advanced Learner's Dictionary

Oxford3000

carrot

noun
carrot pronunciation English ˈkærət carrot pronunciation American ˈkærət
 
1 [uncountable, countable] a long pointed orange root vegetablegrated carrota pound of carrots2 [countable] a reward promised to somebody in order to persuade them to do something
Synonym
incentive
They are holding out a carrot of $120 million in economic aid.It's a big carrot he's dangling in front of Marler's nose.
Idioms

the carrot and (the) stick (approach)

if you use the carrot and stick approach, you persuade somebody to try harder by offering them a reward if they do, or a punishment if they do not
The emphasis is on the carrot of incentive rather than the stick of taxes.